Question : Find the value of $\frac{\cos^2 15^{\circ}-\sin^2 15^{\circ}}{\cos^2 145^{\circ}+\sin^2 145^{\circ}}$.

Option 1: $\frac{1}{\sqrt{3}}$

Option 2: $\frac{1}{1-\sqrt{3}}$

Option 3: $\frac{\sqrt{3}}{2}$

Option 4: $\frac{2}{\sqrt{3}}$

Question : What will be the value of $\frac{\sin 30^{\circ} \sin 40^{\circ} \sin 50^{\circ} \sin 60^{\circ}}{\cos 30^{\circ} \cos 40^{\circ} \cos 50^{\circ} \cos 60^{\circ}}$?

Option 1: $\frac{1}{\sqrt{2}}$

Option 2: $\sqrt{3}$

Option 3: $1$

Option 4: $\frac{1}{\sqrt{3}}$

Question : Using $\cos (A+B)=\cos A \cos B-\sin A \sin B$, find the value of $\cos 75^\circ$.

Option 1: $\frac{\sqrt{5}-1}{4}$

Option 2: $\frac{\sqrt{5}+1}{4}$

Option 3: $\frac{\sqrt{6}-\sqrt{2}}{4}$

Option 4: $\frac{\sqrt{6}+\sqrt{2}}{4}$

Question : What is the value of $5 \sqrt{3} \cos 60^{\circ} \tan 30^{\circ}-3 \cos 0^{\circ}+3 \cos ^2 45^{\circ}+2 \sin ^2 60^{\circ}$?

Option 1: $2\sqrt{3}$

Option 2: $2.5$

Option 3: $3.5$

Option 4: $3\sqrt{2}$

Question : What is the value of $\frac{\tan 45^{\circ}-\tan 15^{\circ}}{1+\tan 45^{\circ} \tan 15^{\circ}}$?

Option 1: $\sqrt{3}$

Option 2: $\frac{1}{\sqrt{2}}$

Option 3: $\frac{1}{\sqrt{3}}$

Option 4: ${\sqrt{2}}$